Problem posing can be a vehicle for inquiry and learning, fostering student creativity and empowerment. One route for supporting meaningful problem posing is through playful math tasks, which can emphasize agency and exploration. We investigated students’ problem posing across three tertiary data sets and found that developing playful math challenges for one another supported instances of discovered complexity, which occurs when students experience and then tackle emergent intellectual and conceptual challenges. We consider the conditions that can foster and constrain the emergence of discovered complexities and discuss how to design environments that are propitious for productive problem posing.